Linear time algorithms for Abelian group isomorphism and related problems

We consider the problem of determining if two finite groups are isomorphic. The groups are assumed to be represented by their multiplication tables. We present an O(n) algorithm that determines if two Abelian groups with n elements each are isomorphic. This improves upon the previous upper bound of O(n log n) [Narayan Vikas, An O(n) algorithm for Abelian p-group isomorphism and an O(n log n) algorithm for Abelian group isomorphism, J. Comput. System Sci. 53 (1996) 1-9] known for this problem. We solve a more general problem of computing the orders of all the elements of any group (not necessarily Abelian) of size n in O(n) time. Our algorithm for isomorphism testing of Abelian groups follows from this result. We use the property that our order finding algorithm works for any group to design a simple O(n) algorithm for testing whether a group of size n, described by its multiplication table, is nilpotent. We also give an O(n) algorithm for determining if a group of size n, described by its multiplication table, is Abelian. (C) 2007 Elsevier Inc. All rights reserved.

Capturability analysis of a geometric guidance law in relative velocity space

In this paper, a relative velocity approach is used to analyze the capturability of a geometric guidance law. Point mass models are assumed for both the missile and the target. The speeds of the missile and target are assumed to remain constant throughout the engagement. Lateral acceleration, obtained from the guidance law, is applied to change the path of the missile. The kinematic equations for engagements in the horizontal plane are derived in the relative velocity space. Some analytical results for the capture region are obtained for non-maneuvering and maneuvering targets. For non-maneuvering targets it is enough for the navigation gain to be a constant to intercept the target, while for maneuvering targets a time varying navigation gain is needed for interception. These results are then verified through numerical simulations.

Four group decodable differential scaled unitary linear space-time codes

Differential Unitary Space-Time Block codes (STBCs) offer a means to communicate on the Multiple Input Multiple Output (MIMO) channel without the need for channel knowledge at both the transmitter and the receiver. Recently Yuen-Guan-Tjhung have proposed Single-Symbol-Decodable Differential Space-Time Modulation based on Quasi-Orthogonal Designs (QODs) by replacing the original unitary criterion by a scaled unitary criterion. These codes were also shown to perform better than differential unitary STBCs from Orthogonal Designs (ODs). However the rate (as measured in complex symbols per channel use) of the codes of Yuen-Guan-Tjhung decay as the number of transmit antennas increase. In this paper, a new class of differential scaled unitary STBCs for all even number of transmit antennas is proposed. These codes have a rate of 1 complex symbols per channel use, achieve full diversity and moreover they are four-group decodable, i.e., the set of real symbols can be partitioned into four groups and decoding can be done for the symbols in each group separately. Explicit construction of multidimensional signal sets that yield full diversity for this new class of codes is also given.

Mapping of Average Shear Wave Velocity for Bangalore Region: A Case Study

Mapping the shear wave velocity profile is an important part in seismic hazard and microzonation studies. The shear wave velocity of soil in the city of Bangalore was mapped using the Multichannel Analysis of Surface Wave (MASW) technique. An empirical relationship was found between the Standard Penetration Test (SPT) corrected N value ((N1)60cs) and measured shear wave velocity (Vs). The survey points were selected in such a way that the results represent the entire Bangalore region, covering an area of 220 km2. Fifty-eight 1-D and 20 2-D MASW surveys were performed and their velocity profiles determined. The average shear wave velocity of Bangalore soils was evaluated for depths of 5 m, 10 m, 15 m, 20 m, 25 m and 30 m. The sub-soil classification was made for seismic local site effect evaluation based on average shear wave velocity of 30-m depth (Vs30) of sites using the National Earthquake Hazards Reduction Program (NEHRP) and International Building Code (IBC) classification. Mapping clearly indicates that the depth of soil obtained from MASW closely matches with the soil layers identified in SPT bore holes. Estimation of local site effects for an earthquake requires knowledge of the dynamic properties of soil, which is usually expressed in terms of shear wave velocity. Hence, to make use of abundant SPT data available on many geotechnical projects in Bangalore, an attempt was made to develop a relationship between Vs (m/s) and (N1)60cs. The measured shear wave velocity at 38 locations close to SPT boreholes was used to generate the correlation between the corrected N values and shear wave velocity. A power fit model correlation was developed with a regression coefficient (R2) of 0.84. This relationship between shear wave velocity and corrected SPT N values correlates well with the Japan Road Association equations.

Polymer drift in a solvent by force acting on one polymer end

We investigate the effect of hydrodynamic interactions on the non-equilibrium drift dynamics of an ideal flexible polymer pulled by a constant force applied at one polymer end using the perturbation theory and the renormalization group method. For moderate force, if the polymer elongation is small, the hydrodynamic interactions are not screened and the velocity and the longitudinal elongation of the polymer are computed using the renormalization group method. Both the velocity and elongation are nonlinear functions of the driving force in this regime. For large elongation we found two regimes. For large force but finite chain length L the hydrodynamic interactions are screened. For large chain lengths and a finite force the hydrodynamic interactions are only partially screened, which in three dimensions results in unusual logarithmic corrections to the velocity and the longitudinal elongation.

Propargyloxycarbonyl as a protecting group for the side chains of serine, threonine and tyrosine

Propargyloxycarbonyl group is used as a protecting group for the hydroxyl groups of serine, threonine and tyrosine. The propargyloxycarbonyl derivatives of these hydroxy amino acids are stable to acidic and basic reagents commonly employed in peptide synthesis. The deprotection of the O-Poc derivatives using tetrathiomolybdate does not affect commonly used protecting groups such as N-Boc, N-Cbz, N-Fmoc, methyl and benzyl esters. The di-and tripeptides synthesized using O-Poc derivatives of serine, threonine and tyrosine are stable, isolable compounds and give the hydroxy peptides in good yields when treated with tetrathiomolybdate.

Prediction of flame liftoff height of diffusion/partially premixed jet flames and modeling of mild combustion burners

In this article, a new flame extinction model based on the k/epsilon turbulence time scale concept is proposed to predict the flame liftoff heights over a wide range of coflow temperature and O-2 mass fraction of the coflow. The flame is assumed to be quenched, when the fluid time scale is less than the chemical time scale ( Da < 1). The chemical time scale is derived as a function of temperature, oxidizer mass fraction, fuel dilution, velocity of the jet and fuel type. The present extinction model has been tested for a variety of conditions: ( a) ambient coflow conditions ( 1 atm and 300 K) for propane, methane and hydrogen jet flames, ( b) highly preheated coflow, and ( c) high temperature and low oxidizer concentration coflow. Predicted flame liftoff heights of jet diffusion and partially premixed flames are in excellent agreement with the experimental data for all the simulated conditions and fuels. It is observed that flame stabilization occurs at a point near the stoichiometric mixture fraction surface, where the local flow velocity is equal to the local flame propagation speed. The present method is used to determine the chemical time scale for the conditions existing in the mild/ flameless combustion burners investigated by the authors earlier. This model has successfully predicted the initial premixing of the fuel with combustion products before the combustion reaction initiates. It has been inferred from these numerical simulations that fuel injection is followed by intense premixing with hot combustion products in the primary zone and combustion reaction follows further downstream. Reaction rate contours suggest that reaction takes place over a large volume and the magnitude of the combustion reaction is lower compared to the conventional combustion mode. The appearance of attached flames in the mild combustion burners at low thermal inputs is also predicted, which is due to lower average jet velocity and larger residence times in the near injection zone.

Semi-empirical procedures for estimation of residual velocity and ballistic limit for impact on mild steel plates by projectiles

This paper deals with the development of simplified semi-empirical relations for the prediction of residual velocities of small calibre projectiles impacting on mild steel target plates, normally or at an angle, and the ballistic limits for such plates. It has been shown, for several impact cases for which test results on perforation of mild steel plates are available, that most of the existing semi-empirical relations which are applicable only to normal projectile impact do not yield satisfactory estimations of residual velocity. Furthermore, it is difficult to quantify some of the empirical parameters present in these relations for a given problem. With an eye towards simplicity and ease of use, two new regression-based relations employing standard material parameters have been discussed here for predicting residual velocity and ballistic limit for both normal and oblique impact. The latter expressions differ in terms of usage of quasi-static or strain rate-dependent average plate material strength. Residual velocities yielded by the present semi-empirical models compare well with the experimental results. Additionally, ballistic limits from these relations show close correlation with the corresponding finite element-based predictions.

Modified density matrix renormalization group algorithm for the zigzag spin-1/2 chain with frustrated antiferromagnetic exchange: Comparison with field theory at large J(2)/J(1)

A modified density matrix renormalization group (DMRG) algorithm is applied to the zigzag spin-1/2 chain with frustrated antiferromagnetic exchange J(1) and J(2) between first and second neighbors. The modified algorithm yields accurate results up to J(2)/J(1) approximate to 4 for the magnetic gap Delta to the lowest triplet state, the amplitude B of the bond order wave phase, the wavelength lambda of the spiral phase, and the spin correlation length xi. The J(2)/J(1) dependences of Delta, B, lambda, and xi provide multiple comparisons to field theories of the zigzag chain. The twist angle of the spiral phase and the spin structure factor yield additional comparisons between DMRG and field theory. Attention is given to the numerical accuracy required to obtain exponentially small gaps or exponentially long correlations near a quantum phase transition.

Smoldering combustion of "incense" sticks - Experiments and modeling

This paper is concerned with the experimental and modeling studies on the smoldering rates of incense sticks as a function of ambient oxygen fraction in air, the flow velocity and size. The experimental results are obtained both for forward and reverse smolder conditions. The results are explained on the basis of surface combustion due to diffusion of oxygen to the surface by both free and forced convection supporting the heat transfer into the solid by conduction, into the stream by convection and the radiant heat transfer from the surface. The heat release at the surface is controlled by the convective transport of the oxidizer to the surface. To obtain the diffusion rates particularly for the reverse smolder, CFD calculations of fluid flow with along with a passive scalar are needed; these calculations have been made both for forward and reverse smolder. The interesting aspect of the CFD calculations is that while the Nusselt umber for forward smolder shows a clear root( Re-u) dependence ( Re-u = Flow Reynolds Number), the result for reverse smolder shows a peak in the variation with Reynolds number with the values lower than for forward smolder and unsteadiness in the flow beyond a certain flow rate. The results of flow behavior and Nusselt number are used in a simple model for the heat transfer at the smoldering surface to obtain the dependence of the smoldering rate on the diameter of the incense stick, the flow rate of air and the oxygen fraction. The results are presented in terms of a correlation for the non-dimensional smoldering rate with radiant flux from the surface and heat generation rate at the surface. The correlations appear reasonable for both forward and reverse smolder cases.

Velocity-Space Contours of Collision Integrals

Based on the recently found closed-form expressions of the Boltzmann collision integrals in a rigid-sphere gas for multi-Maxwellian distributions, a few typical sets of contour surfaces of the integrals in the space of molecular velocities are presented. These show graphically the tendency toward equilibrium under the influence of collisions. A brief preliminary comparison with Monte Carlo results is also given.

NMR study of internal motions in certain iron group fluosilicates

NMR study of ferrous fluosilicate hexahydrate indicated the presence of motion of both proton and fluorine nuclei. Only a single narrow line was observed for protons for any arbitrary orientation of a single crystal with respect to the applied magnetic field. This can be interpreted in terms of a phase-correlated flip motion of the interproton vectors between two disordered orientations or in terms of a hindered rotation of the Fe(H2O) 6 octahedron about the fourfold axes, together with the flip motion. The fluorine second moment indicated that the SiF6 octahedron also is undergoing reorientation. The temperature variation of the powder linewidth showed a transition around 195°K and led to rather low values for the potential barriers hindering the motions. No significant temperature variation of the linewidth was observed for hexahydrated cobalt fluosilicate in the temperature range between 90°K and room temperature. Similar observations in a powder sample of tetrahydrated copper fluosilicate also showed the presence of internal motions. The linewidth transition in this case took place at about 220°K and was found to be rather abrupt. The potential barrier for the motion was found to be relatively high.

Sound Velocity Anomaly at the Mott Transition: Application to Organic Conductors and V2O3

Close to the Mott transition, lattice degrees of freedom react to the softening of electron degrees of freedom. This results in a change of lattice spacing, a diverging compressibility, and a critical anomaly of the sound velocity. These effects are investigated within a simple model, in the framework of dynamical mean-field theory. The results compare favorably to recent experiments on the layered organic-conductor kappa-(BEDT-TTF)(2)Cu[N(CN)(2)]Cl. We predict that effects of a similar magnitude are expected for V2O3, despite the much larger value of the elastic modulus of this material.

GMRT observations of the group Holmberg 124: Evolution by tidal forces and ram pressure?

We report new radio continuum and 21 cm HI observations using the Giant Metrewave Radio Telescope (GMRT) of the group Holmberg 124 ( Ho 124) comprising four late-type galaxies, namely NGC 2820, Mrk 108, NGC 2814 and NGC 2805. The three galaxies, NGC 2820, Mrk 108 and NGC 2814 which are closely located in the sky plane have clearly undergone tidal interactions as seen from the various morphological tidal signatures and debris. Moreover we note various features in the group members which we believe might be due to ram pressure. In this paper, we describe four interesting results emerging from our observations: a) detection of the tidal radio continuum bridge at 330 MHz connecting the galaxies NGC 2820+ Mrk 108 with NGC 2814. The radio bridge was discovered at 1465 MHz by van der Hulst & Hummel ( 1985, A& A, 150, 17). We find that the bridge has a fairly steep spectrum with a spectral index alpha(S proportional to nu(alpha)) of - 1.8(-0.2)(+0.3) which is much steeper than the - 0.8 quoted by van der Hulst & Hummel ( 1985); b) detection of other tidal features like the tilted HI and radio continuum disk of NGC 2814, a HI streamer and a radio continuum tail arising from the south of NGC 2814. We also report the detection of a possible tidal dwarf galaxy in HI; c) sharp truncation in the HI distribution in the south of NGC 2820 and in the HI and radio continuum distribution in the north of NGC 2814. The optical disks in both the cases look undisturbed. As pointed out by Davis et al. ( 1997, AJ, 114, 613), ram pressure affects different components of the interstellar medium to varying degrees. Simple estimates of pressure in different components of the interstellar medium ( radio continuum, Ha and HI) in NGC 2820 indicate that ram pressure will significantly influence HI; d) detection of a large one-sided HI loop to the north of NGC 2820. No radio continuum emission or Ha emission is associated with the HI loop. We discuss various scenarios for the origin of this loop including a central starburst, ram pressure stripping and tidal interaction. We do not support the central starburst scenario since the loop is not detected in ionized gas. Using the upper limit on X-ray luminosity of Ho 124 (Mulchaey et al. 2003, ApJS, 145, 39), we estimate an upper limit on the intragroup medium (IGrM) density of 8.8 x 10(-4) cm(-3). For half this electron density, we estimate the ram pressure force of the IGrM to be comparable to the gravitational pull of the disk of NGC 2820. Since tidal interaction has obviously influenced the group, we suggest that the loop could have formed by ram pressure stripping if tidal effects had reduced the surface density of HI in NGC 2820. From the complex observational picture of Ho 124 and the numerical estimates, we suggest that the evolution of the Ho 124 group may be governed by both tidal forces due to the interaction and the ram pressure due to motion of the member galaxies in the IGrM and that the IGrM densities should not be too low (i.e. >= 4 x 10(-4)). However this needs to be verified by further observations.

The 5-Methyl Group in Thymine Dynamically Influences the Structure of A-Tracts in DNA at the Local and Global Level

DNA sequences containing a stretch of several A:T basepairs without a 5'-TA-3' step are known as A-tracts and have been the subject of extensive investigation because of their unique structural features such as a narrow minor groove and their crucial role in several biological processes. One of the aspects under investigation has been the influence of the 5-methyl group of thymine on the properties of A-tracts. Detailed molecular dynamics simulation studies of the sequences d(CGCAAAUUUGCG) and d(CGCAAATTTGCG) indicate that the presence of the 5-methyl group in thymine increases the frequency of a narrow minor groove conformation, which could facilitate its specific recognition by proteins, and reduce its susceptibility to cleavage by DNase I. The bias toward a wider minor groove in the absence of the thymine 5-methyl group is a static structural feature. Our results also indicate that the presence of the thymine 5-methyl group is necessary for calibrating the backbone conformation and the basepair and dinucleotide step geometry of the core A-tract as well as the flanking CA/TG and the neighboring GC/GC steps, as observed in free and protein-bound DNA. As a consequence, it also fine-tunes the curvature of the longer DNA fragment in which the A-tract is embedded.